Identifiability in Measurement Error Models

Abstract

Identifiability is a fundamental issue in measurement error models, because consistent estimation of all unknown parameters in the model is impossible if it is unidentifiable. In this Chapter we study this issue in linear and nonlinear regression models with either classical or Berkson type measurement error. We use a simple linear model to demonstrate how the measurement error in covariates causes its non-identifiability. We show that the nonlinear models with Berkson measurement error can be identified without prior restrictions on the parameters or extra data besides the main sample. We also show that the classical measurement error (errors in variables) models can be identified using the instrumental variable approach and provide a sufficient rank condition for the identifiability. Some examples are provided for illustration.